princessss wrote:At a technology consulting firm with x computers, all of which are laptops or destkops, 30% are laptops; if 80% of the total number of computers have more than 1GB of RAM and 10% of the computers with less than 1 GB of RAM are laptops ( and no computers have exactly 1GB of RAM), approximately what percent of destkops have more than 1GB of RAM?
A) 75%
B) 60%
C) 52%
D) 40%
E) 45%
I tried to solve this problem by plugging in.
If X is 100, than total number of lapotps would be 30 and total number of destkops would be 70.
But the correct answer is A.
I don't get how can that be the correct answer if there are supposed to be only 70 destkops total. Why doesn't plugging in work for this problem?
Whenever we have groups (in this case, laptops and desktops) that are being divided into smaller groups (in this case, those with more than 1GB of RAM and those with less), we can use a
group grid to organize the data. Here's what the grid looks like:
_______________laptop______desktop_______Total
>1GB:
<1GB:
total:
In the grid above, every row has to add up to the total, as does every column.
Looking at the top row, laptops with more than 1GB + desktops with more than 1GB = total with more than 1GB.
Looking at the left-most column, laptops with more than 1GM + laptops with less than 1GB = total laptops.
Now let's fill in the data step by step. Whenever we have 2 entries in a row or column, we can determine the remaining entry, since everything has to add up horizontally and vertically. Let's plug in 100 for the total number of computers:
__________laptops______desktops_______Total
>1GB:
<1GB:
total:_________________________________100
30% are laptops:
____________laptops______desktops_______Total
>1GB:
<1GB:
total:____________30__________70________ __100
80% have more than 1GB:
______________laptops______desktops_______Total
>1GB:______________________________________80
<1GB:______________________________________20
total:______________30__________70____ _______100
10% of the computers with less than 1GB are laptops:
_______________laptops______desktops_______Total
>1GB:_____________28__________52___________80
<1GB:_____________2___________18___________20
total:______________30___________70______ ___ 100
Notice that everything adds up horizontally and vertically. Neat!
(Desktops with >1GB)/(Total desktops)*100 = (52/70)*100 = 75 approximately.
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